Predicting the cost of any decision \(x\)  (or parameter choice \(\theta \)  in the context of machine learning, Example REF ) is typically merely a means to derive an approximation of the optimal solution and its cost.
Out-of-sample guarantees of the form (REF ),
which hold pointwise for any decision \(x\) , do not generally hold for the prescribed decision with minimal estimated cost
\(\operatornamewithlimits{arg\,min}_{x \in \mathcal {X}} \hat{c}(x,\hat{\mathbb {P}}_T,T)\) .
An indirect way to impose out-of-sample guarantees on the prescribed decision is to derive a uniform counterpart to (REF ) which holds uniformly for all decisions.
To do so in statistical learning, one typically restricts the considered function class \(\lbrace f_{\theta }\rbrace _{\theta \in \Theta }\)  to be of controlled bounded complexity, as measured by covering numbers or VC dimension [1]}, [2]}.
When the purpose of decision-making is only to derive the optimal solution of problem (REF ), seeking such uniform bounds seems unduly restrictive. We seek, therefore, to investigate cost estimates satisfying out-of-sample guarantees precisely at the prescribed decision instead of uniformly over all decisions. In the following, we formalize these observations in what we call the prescription problem.
